Preparation for the 21st C and the Information Era. What our kids SHOULD be learning!

[Alexander]

In another thread, this subject cropped up. It is something that I believe is too important not to have it's own thread.

I hope it will be a place where those not yet familia will be able to ask questions or post their own observations.

Originally posted by larsy

Alexander, I for one would be glad to hear more about the skills needed for the Information Age over the Industrial.

Origionally posted by Wildflower
I could go on, I've been doing a lot of research on unschooling and its benefits over public ed lately...Alexander, I'm also interested in what you mentioned about the Information Age...


Hi guys,

sorry for the delay in reply.

Actually I consider it to be the Information Era, not Age, because, as I understand it, an Age is shorter than an Era. What we are entering now, is surely to last longer than the Industrial Age, which really started only in the mid 19th Century, and is all but over in the US and Western Europe.

As for the skills that are required, they are things like:

Problem Solving,

Being Self Motivated and Self Directed,

Being able to set your own goals,

Being able to take Responsibility for things,

Being able to Identify Choices,

Having Interpersonal skills, (negotiational skills, bargaining skills, team-work and management skills, and family skills)

Being able to take on New Skills easily and quickly, that enable you to achieve your goals.

And if you are not a speaker, English, todays "lingua Franca".

There are more, and I have written about it before, so I'll see if I can find it and post it. Anyone got any other ideas?

BTW, you will notice that I do not include things like reading, writing, arithmetic, computer skills, science or knowledge of the internet. The assumption that these are needed is an Industrial Age mind-set.

The truth of the matter is that these may, at the moment, be important skills for survival and day to day living, but non of them are certain to retain any relevance in the Information Era. Indeed, I am not the only person to argue that what is mis-named as "Math" in modern American schools, is an acute waste of time. Real Mathematics is found almost nowhere in any curriculum in most of the Industrial world. UK schools made a brave attempt in the late 70's and early 80's, but it did not penetrate everywhere, and it was soon diluted. The worst culprits, (or victims) are the Japanese, Koreans and the Singaporese.

Looking forward to more comment on this.

a

a

[Lucy]

ok, so whats wrong with the math? I would love to know since I have been doing singapore math with dd (5), we homeschool. It looks very real to me, hands on, real world stuff so far, but of course this is a very early level.

Would love to hear what exactly you mean.

Thanks!:)

[truly_sarah]

Alexander, yes. I'm very interested too to know what's the matter with the Singapore Math. Your ideas are usually well presented and thought out and have a firm foundation, so I will consider very carefully any facts/ideas you have to offer.

Why are these countries both victims and culprits simultaneously? How should math be taught ideally?

I am always tinkering around in my head with a number system that is based on a spiral number line instead of a straight line. When the teacher first presented the number line in first grade (I remember well the day) I found it suspicious, since in the real universe there are no straight lines. But it was intellectually challenging to go along with the mental gymnastics and computations of the system presented and it has of course served me well - my checkbook computations match up pretty well with the ones suggested on the back of my monthly statements!

I'm thinking about reading Flatland with my son...isn't that the name of the book that shows everything in 2 dimensions? I would someday like to explore different numbering systems with him and math as logical thinking instead of just numbers and rules/axioms/theorems. Is that what you mean?

Sarah

[Dot.mom]

Alexander, do tell!!!!! Math and how it is taught is something that really interests me. My father is a mathematician and taught my brother and I in a way that made public school math seem rediculously uninspired and limited when we finally got there. Unfortunately, we then did very poorly.

[Alexander]

OK.

I can't just give "the" answer straight and complete, it is too boring to just have to wade through. (+ time. I'm really busy trying to start the home page for our school :D)

But I have read you posts, and would love to find time to address you all.

But to come back to the subject. Math isn't Maths. What you are dealing with is arithmetic. Got that? The manipulation of numbers, (angles for geometry).

And if you wish to ensure that your children learn to do that, then it is a noble cause, and I for one will not critisize it at all.

But it is arithmetic.

And this will do little for someone growing up in the Information Era.

Mathematics is not only about the relationship of ideas, and how these inter-relate, but also about the way people discover and internalize these concepts. Notice the word "concepts" here, not numbers.

There are 2 ways to "teach" too.

1) you can show by demonstration that something is true / exists / is beautiful etc, or

2) you can create an environment inwich a child "comes across" the same.

1) Industrial. Easy. Done for a purpose.

2) Information. Hard. done only because a student's nose takes them there.

How can we have maths with no numbers?

How do I count the ways? :D LOL (that was a joke ok! ;) )

Take prime numbers.

First, is it important that any child MUST know what these are?

2nd, does it have to be numbers that are covered in a curriculum? (the concept can be covered spacially)

3rd surely, the thoughts of a child that recognised what they (primenumbers) are, through their own volition, and can recognise any connections to anything else, is deeper than that of a person that has simply been told and remembered what they are?!. . . Indeed, such a child has indulged in mathematics, not "Math".

Suppose I presented a lesson on prime numbers that invoved NO NUMBERS! Would that be acceptable to those teaching "math"?

I have actually created such a lesson. And thus far, found Industrial Age "Math" teachers very uncomfortable with it.

I even "gave" the lesson to a Junior Professor of Mathematics here in Japan, and it took a goo hour (and some hints, coaxing and prodding) before he saw what he had been studying. Of course when he understood that we were dealing with primes, he could use his own internal model to quickly solve all the problems, and my little "lesson" became redundant.

BUT the style gave new insite to this gentleman, and he loved it.

So, I say that real Mathematics is about the discovery of manipulations and relationships, not having them presented to you so you don't have to think about too much. Anything that is given to you that becomes self evident is junk.

Of course I have heard many argue that in the "real world" we don't need that many mathematitians.

Well, in the "Information World" we sure don't need people that rote learn their times tables!!!!!

Get real guys, even the Japanese use calculater to add up the price of your coffee and cake!

There is much I have not addressed. I'll get round to it.

I am very aware that not everything I have written is clear, and I appologise. Please DO bug me about the bits that come across lumpy. (It's 1:30 am now, so I must get to bed).

Truly Sarah:

Spiral? Wow! Internalized or what. Great! :D

Dot.Mom, you have no idea how close we really are. I hear you! My old man (http://www.mth.kcl.ac.uk/~streater/)

Hope this begins to help, but if not, feed-back please.

a

Edited slightly for grammatical clarity.

a

[sleepies]

WoW that post went right over my head
guess it is a good thing im not home-schooling.
maybe it was the fact i got only formula and not breastmilk....that i don't understand.

what are you talking about?

oh. im sure it is me and not you.

but, im lost

[truly_sarah]

Reading a book like Flatland might be a start...but Alexander, we want to see the lesson plan, or some other details of what you're talking about. My imagination won't stretch that far today and I'm going to accuse you of maliciously teasing us...oh far worse than the scent of mere chocolate or coffee!

Thanks in advance.

Sarah

[Lucy]

sleepies, oh no its not just you, unless its just me and you. lol!

If you could be a little more precise Alexander I would love it!:)

btw I use my memorized times tables all the time to calculate stuff in my head, like at the store ect.

Now if by creating the environment where a child can learn a fact you mean for instance, letting them help you bake a cake and measure the ingriedients and as a result learn fractions, instead of learning from a worksheet, than I understand and agree with you that much. Is that st like you mean?:confused:

[larsy]

hey, Alexander, thanks for posting on this! :) I agree! It's great to see this articulated- I'm been stumbling around in this and not seeing the forest for the trees.

short on time now- I just got a copy of Flatland, thanks for reminding me of it! We just got a hold of 'The I hate Mathematics Book' and 'Math for Smarty Pants' and 'The Book of Think' and various others by these same authors. I think these are definately going in the right direction! We have devoured these and use the concepts daily. What fun! :)

gotta run, thanks!
larsy

[dfoy]

Alexander,

I'm a teacher, too. Taught "math" to special education kids for years (I am in collaborative classes all day teaching high school science now and making the regular curriculum accessible to students with special needs). I agree, its the concepts that count (no pun intended). Same thing with grammar. Do kids really need to know what a gerund is to write a good paragraph? Of course not!

Students do need to know that the answer that they get on their calculator makes sense for the information they are asked to get. You teach that through concepts, not repitition or drill.

Mathematics is patterns. I learned a lot about math when I was little through music (time signature, augmented 5ths, etc) since my mother was a musician.

[Alexander]

Originally posted by Lucy
sleepies, oh no its not just you, unless its just me and you. lol!
If you could be a little more precise Alexander I would love it!:)



Precision is on it's way. ;)


btw I use my memorized times tables all the time to calculate stuff in my head, like at the store ect.


and I question if that is needed in this day and age. Should we be allotting a good part of childhood to this activity?

I say no. In fact I say ABSOLUTLY NOT! We are wasting life no less. :crying


Now if by creating the environment where a child can learn a fact you mean for instance, letting them help you bake a cake and measure the ingriedients and as a result learn fractions, instead of learning from a worksheet, than I understand and agree with you that much. Is that st like you mean?:confused:

No.

This is a good environment for teaching arithmetic, not mathematics, although some mathematics will creep in by itself, but not because of the adults or the corse, but because of the child's observation of the natural world around them.

Gotta fly.

a

[Lucy]

thanks for responding Alexander. I still do not have a clear idea of what you mean by real mathematics. I must say I do not feel a lot of my childhood was spent memorizing times tables, it was relatively easy for me, and I am glad I have them memorized. Too often I have been in a checkout where the register isn't working properly for some reason, and the poor clerk has to do the math herself. Most times it has been a painful struggle. I appreciate when people can add, subtract, multiply and divide properly. I still think these are valuable skills. Now how much time should we devote to them? I don't think its the ? of too much time in the public schools being spent on arithmetic, I think there is just too much wasted time, where the kids aren't doing anything of value, waiting, ect.

What would your alternative approach to mathmatics be?

Forgive me if this is tiresome too you.

[Alexander]

File c

lucy said:
ok, so whats wrong with the math? I would love to know since I have been doing singapore math with dd (5),

Nothing is "wrong" with it, but you are deluding yourselves if you think you are teaching mathematics.


lucy also

It looks very real to me, hands on, real world stuff so far...

Yes, but is arithmetic.

Hope this is starting to help

a

[Alexander]

file d

truly_sarah said:

Why are these countries both victims and culprits simultaneously? How should math be taught ideally?

Victims because they can not let go of the Industrial Age Model, for which "Math" (note no 's') was seen as a necessary component. Not only that, but in the race to be the best, children are force fed this tripe at a rate that is far quicker than they are really able to digest. Ask any adult or teen to solve problems commonly given to 10 year olds, and they will fail miserably. This begs the question, why were they taught the stuff in the first place???!

Culprits because they not only waste the life of children, but they are neglecting to equip these children with the skills that are really needed in the Information Age, beginning with creativity. Not only that, but they continue to help perpetuate the misconception that all that Math is really necessary.


truly_sarah also said:

I am always tinkering around in my head with a number system that is based on a spiral number line instead of a straight line.



This is most interesting. It demonstrates a most un-usual internalization of numbers. It is a shame that that was not understood as your model by your teacher and cultivated. That would have been the "ideal" way to do Maths (note the extra 's' to denote "mathematics").

truly_sarah also said:

my checkbook computations match up pretty well with the ones suggested on the back of my monthly statements!

A common enough sentiment, if not comment! :) But the fact is that you use arithmetic for that, not mathematics. And it may be a stunning revelation to many, but you do not have to begin teaching children this (arithmetic) until they become teenagers, if at all. They will all get there on their own, with or without wasting many hours of their lives in class doing it.

truly_sarah also said:

I'm thinking about reading Flatland with my son...isn't that the name of the book that shows everything in 2 dimensions? I would someday like to explore different numbering systems with him and math as logical thinking instead of just numbers and rules/axioms/theorems. Is that what you mean?



I am unfamiliar with the book, but the title strikes great resonance with me. As a child, my brother and I talked at great length about what it would be like to live in "flat-land" and what the experiences of beings in such a place would be like. We even drew pictures of what they could look like, and their insides an' all.

Exploring numbering systems? Hmmm. It depends on how you approach this. I'll come to this in a mo.

Math maybe logical. Mathematics (is rarely?) is not always (only the proofs are). Mathematics often gut instict, guess, idea, image and trial and error. It's more like composing music. When you get it right, it is beautiful.

In fact that is a good analogy. Mathematics is like composing music. What you teach as "Math" is playing it.

As for covering the different ideas in Mathematics (dimensions, geometry, bases, number theory): that is more like getting someone to be able to sing along with a bit of Mozart, or recognise that is Beathoven, or play Smetina well.

You don't need Mathematics to balance your books, you need arithmetic (commonly called "Math").

Getting there

a

[Alexander]

file e

Dot.mom said

Alexander, do tell!!!!! Math and how it is taught is something that really interests me. My father is a mathematician and taught my brother and I in a way that made public school math seem ridiculously un-inspired and limited when we finally got there. Unfortunately, we then did very poorly.

Once again, the term "math" which I see as a misnomer for arithmetic. Again, the methods refined over the last 150 years are probably fine. But mathematics? That is hard. To start with, kids have to have the right mind, the curiosity that leads them in this direction. If they do not have this, you have nothing.

I had an unbelievably bad teacher in HS, and I dropped out of Math. My teacher would not listen, had an agenda, a time table, and wanted to be the "star" in his own class. Ironically, leaving probably saved me, though I had to do much of this stuff again to solve dynamic circuits in collage, but it was quickly forgotten, as soon as the tests were over!

When I was brought to Japan, I was sent to the Computer Aided Design Dept. and became involved in writing CAD software. And look! I could not remember a single trig formula :o

So I started working from first principles. Boy I was slow! But, unlike the other engineers (who were coding much faster than me because they could recite all the formula and just type out the code), I also thought about how the curves on the screen would be translated to the final machine cutter. I doubt I would have done this if I had been just typing out the code like everyone else. This "other thought" saved us from a monumental error.

a

[truly_sarah]

So, you are saying...it is OK to teach the Arithmetic when the kids do need it...my son at 11 has a checkbook and uses it, and he cooks, and does other stuff - ie figuring out how much food his dog needs for his weight, and so forth, that does require Arithmetic. He is really good at figuring discounts in his head, doing exchanges of money from US-Canadian and back, computing interest and ROI, and figuring how much time it will take to bushwack at x kph distance Z1 versus follow trail at y kmp distance Z2. For his life, which is still pretty far away from a lot of technology, it makes sense for him to be able to do calculations. He is interested in maps and is my navigator on road trips. If he couldn't do the figuring, we'd literally be lost. His knowledge is such that oftentimes, I do not even bother to consult the map, I just drive and he gives directions, complete with ETAs to landmarks. That is great.

There is something else going on in there though, because when he does his Singapore Math (no S!) I look at his workbook, and many times, for a word problem, he will have an answer, and nothing else. They are problems that I would probably have to write down simultaneous equations for! (And I am not what you would consider mathematically challenged.) I have to check my impulse to ask him to do it the 'correct' way, and thinking 'oh, he will get into trouble when he comes up against more complicated problems and needs to know how to write and solve simultaneous equations. Somehow, he "sees" the answer and has a worthwhile system of deducting the answer. (This is a book with no answers in the back, so I know he's not getting it there.) That was a BIG LEAP for me. Leaving WELL ENOUGH (or MUCH BETTER) alone because it didn't jive with what I believed internally. I don't actually teach him with his curriculum, he's a self-learner...I give him the book and he is motivated enough to do it...if he has a question, it's answered the way my brain works, not necessarily his, and then he knows me well enough to understand how I see things, then he somehow translates into his way of thinking, and eventually, 'gets' it.

I know that he has some roller coaster programs that he plays around with, and has been reading up on G forces and velocity and doing some experimentation. At some point, he is going to get bored with the canned packages and we will have to get him a CAD program to play with.

OK all you math and music people...I have had an idea about a statistical package that incorporates both, for looking at complex data sets...I would call it the statischord! Basically, you could load your data set into a big solution space (that does not have to be, and is better if it is not - symmetrical, or even a matrix), and select a 'harmony key' that best suits your brain's natural resonance. Then you could select different instruments for each variable, and navigate through the solution space listening for concordance/discordance or interesting sequences...the idea being that where there is some sort of basic correlation between states of variables, you would hear a 'theme' and where there are interesting spaces or points of intersection, you would hear something different, and would be able to intuitively tell (because it is 'tuned' to your own resonance) which variables were involved and in what state. Personally, I think it would be much easier than poring over printouts...and if you wanted to share with someone with a different resonance, all you would have to do is switch keys. In the same way, somebody who deals better with color could use colors instead of sound (but colors HAVE sound, right, in the way they affect your brain, they do produce waves that could be translated...) I know I'm not the only person who's ever had this idea! I wonder if anyone knows if there is anything like this in development or even available now? It would be fun to try it out!

Alexander, yes, that's what Flatland is about...just like you imagined as a child.

Still interested in that lesson plan though!!!

Sarah

[Alexander]

file f

sleepies said:

WoW that post went right over my head guess it is a good thing im not home-schooling. maybe it was the fact i got only formula and not breastmilk....that i don't understand.

what are you talking about?

oh. im sure it is me and not you.

but, im lost



It is certainly not you. The difficulty in understanding what mathematics is, is shared by those purporting to be educationalists in your local and state government. And they haven't got it right either. Not even close. :rolleyes:

It is hard. So don't think any the less of yourself for struggling here.

As for not Home schooling. Sadly, I think that it would be much better if you were to. Then you could just ignore the whole subject. ;)

a

[larsy]

re: homeschooling, Alexander, amen!

[Lucy]

so is that your reccommendation, that we ignore arithmetic?

Do you teach math? Or do you discover this on your own?

[parisfrance]

Alexander, have you ever read "Goedel, Escher, Bach"? It's about the connections between math, art, and music. I haven't read it yet, but my brother highly recommends it (and the authors second book whose title escapes me).

[larsy]

I don't think we can ignore arithmetic, it is something that we use daily. And in the process of using it, the kids learn about it. When they are interested in it, they learn it quickly. No need to do all the drill and repitition. All the time can be much better spent!

[Wildflower]

wow! this is really exciting! this helps my mind so much! so, this means that, as unschoolers, my kids can learn arithmetic through our everyday activities as they need/want to, and if they have some brillant, genetically-suprising careers as architects/engineers/mathmaticians destined for them then they will naturally gravitate to these feilds without me nudging them towards formal "math" drills etc...

See, I've been so inspired my by study of "unschooling" except for this nagging fear that no math will ever happen in our house without some formal work on it, and then what if they never get to discover some great talent they might have in a math feild...

but I went up to calculus in high school, and have forgotten all but the most general of impressions of what it all was about, and not used any of it! what a waste!

i will not demand that dd spend a second of her precious life doing anything that she does not choose because it interests and empowers her.

and that's my feeling about our new age whatever you call it: now its more important to love learning in general than to have learned anything specific, because then you can always dive in and learn whatever arises that you need.

more important now to know yourself, know who you are and what you want each moment. instead of just knowing your tables and rules and facts which might not even matter to you ever.

[k'smami]

Ok. So I'm compiling a list of books to read on the subject because this stuff is really compelling and I need to do a lot more reading if I'm going to really understand what you're talking about. So far you have...

Flatland
The I hate Mathematics Book
Math for Smarty Pants
The Book of Think

Any more? Any websites?

[lauren]

:) A very gentle reminder to all, to keep posts respectful and curious, especially when feeling frustrated or confused.

While I have no specific info. to add to this discussion of arithmetic vs. math vs. maths, it is a fascinating and eye opening inquiry. Let's continue to ponder it in the spirit of learning.

[Alexander]

Originally posted by Lucy
so is that your reccommendation, that we ignore arithmetic?



Absolutly. Unless a child either shows a natural inclination to do it, or towards methematics, or if that child requests such assistance.


Do you teach math? Or do you discover this on your own?

Terminololy terminology.

Math=arithmetic (+ bits)
Maths=mathematics

You can teach Math.

You can't teach Mathematics. (Well not easily anyway)

People do discover it on their own. Even we ordinary mortals who are not destined to become Professors! We do it quite naturally.

a

[Alexander]

Originally posted by parisfrance
Alexander, have you ever read "Goedel, Escher, Bach"? It's about the connections between math, art, and music. I haven't read it yet, but my brother highly recommends it (and the authors second book whose title escapes me).

Never heard of them, and getting good books out here is a little hard. I'll keep my eyes open the next time I'm in the UK, or if I get to Boston this summer.

a

[Alexander]

Originally posted by larsy
I don't think we can ignore arithmetic, it is something that we use daily. And in the process of using it, the kids learn about it. When they are interested in it, they learn it quickly. No need to do all the drill and repitition. All the time can be much better spent!

Quite right. We do not drill our children to walk at 6 months so thaey can take the opportunity to become olympic runners!

The very fact that children face it everyday in their real lives means they will get a grip on it.

And if they don't encounter it everyday, then by default, no need to do it.

a

[Alexander]

Originally posted by Wildflower
wow! this is really exciting! this helps my mind so much! so, this means that, as unschoolers, my kids can learn arithmetic through our everyday activities as they need/want to, and if they have some brillant, genetically-suprising careers as architects / engineers / mathmaticians destined for them then they will naturally gravitate to these feilds without me nudging them towards formal "math" drills etc...

Snip. . .

more important now to know yourself, know who you are and what you want each moment. instead of just knowing your tables and rules and facts which might not even matter to you ever.

1 million exactly s.

Your post is SO brilliant, everyone should read it. (http://mothering.com/discussions/showthread.php?s=&postid=36996#post36996)

a

[Alexander]

Originally posted by k'smami
Ok. So I'm compiling a list of books to read on the subject because this stuff is really compelling and I need to do a lot more reading if I'm going to really understand what you're talking about. So far you have...
Flatland
The I hate Mathematics Book
Math for Smarty Pants
The Book of Think
Any more? Any websites?

Careful now. The thread was designed to look at the skills required for the Information Era, of which our comprehension of what mathematics or Math we should teach is a part. (not that I mind the current direction of the discussion at all)

What I want to say is that is is not only math (or mathematics) that we need to re-think when we prepare our children for the 21st C.

It is everything that we currently describe as education.

Thus, a general case (Now that's mathematics ;) ) needs to be understood.

As for books. . . I would sell you mine, but before I could finish it, I discovered someone else had already done the job :rolleyes:

this site to look at some online chapters (http://www.sudval.org/books.html)

but you need to read Free at Last.

By the same author

http://www.mothering.com/14-0-0/html/14-1-0/14-1-democraticschools103.shtml

Anyone who is reading this book could create a Discussing Free at last Thread. I'll join :)

a

[Alexander]

Originally posted by Just Wondering
IMO.........This whole discussion is a total waste of time, Alexander, until you define what you mean by REAL MATH. I tried to find a definition of this by reading through your verbiage in file a to file f. There was nothing.

Snip

So until you actually define yourself precisely, so that people can understand what you mean, the discussion is totally frustrating and confusing. To the point of being a waste of time, if nothing postive or useful can be taken out of it.

Well everything I snipped I basically agree with.

As for a definition, I want to start a new thread for that. This is not meant to be a discussion an what Mat or maths is per se. I am trying to keep up with all these wonderful posts!

As for it being a waste of time? No. We are just miandering to the right (or better) answer.

This is new ground for many. Not all our ideas are fully formed, and if I were to just jump to the end, I'd lose people.

That can easily happen.

But a definition. Yes. I'll set up a new thread soon.

a

[Alexander]

Originally posted by truly_sarah

Alexander, we want to see the lesson plan, or some other details of what you're talking about.


Sarah

OH Juice!!

OK. I have many. Can I get back to you on this?

Phew! I think I caught up :p

a

[Britishmum]

Alexander - I came over here from your link on the times tables thread, where you say that learning tables is time wasted in this day and age. I don't have time to wade through this entire thread; I tried but found it extremely dificult to follow!

Anyway, I just asked dh if he needs times tables in his work, which is at the cutting edge of technology. He laughed and says that he uses them all the time. Certainly, he could do his job without them, but he would be slow and ineffective and not contribute to the team in the way that is expected. (and would probably not be useful enough to the team to be employed by them!)

Apparently the mental dexterity to manipulate numbers is essential. Often he has to mentally computer a load of figures to decide which direction to take before calculating accurately. He uses times table knowledge to do this all day every day. If he didn't have the knowledge, he would spend more time calculating and less time being creative. In team settings it would be impossible to contribute if you couldn't just 'see' the approximate answers to these sorts of problems in your head.

I once went to a lecture once on accelerated learning with him. The speaker gave a quick maths 'quiz' where he demonstrated that the brain often 'tricks' you by seeing what it thinks it should see, not what the eye actually sees. Dh was the only person in the room who didn't get the wrong answer. He just 'saw' the correct solution, in the way that you say that you had a feel for CAD. He couldn't understand why others got it wrong.

I just can't see how knowing times tables along with understanding them cannot be an essential tool for this century. Even if you don't do the same sort of work as my husband, don't we all need to balance our cheque books, split bills in restaurants, work out how many potatoes we need for a dinner party, and so on and so on? I"m not advocating hours spent in drilling children in times tables, and believe that there are faster and more fun ways of learning them, but I can only imagine how incompetent we'd all be if we needed a calculator for all these everyday things.

[Alexander]

Originally posted by Britishmum
Alexander - I came over here from your link on the times tables thread, where you say that learning tables is time wasted in this day and age. I don't have time to wade through this entire thread; I tried but found it extremely dificult to follow!

No.

I didn't say that it was a waste of time for everyone. Just those who end up not needing it in the end ( almost everyone). My point is that we learn much that becomes redundant knowledge. We are able to learn what we need when we need it.

I think you'll find we are madly agreeing with each other.

The rest of your post concerning your DH, and his need to continuously use tables etc, nicely strengthens my point. Those that need to use them, do.

Indeed, the illustration you provide of the seminar on accelerated learning goes further to re-confirm my point. Those that do not continuously use a particular branch of mathematics (or music or literature or cooking) are not practiced, and struggle.

How much intelect does it really take to learn the tables? Almost nothing.

The knowledge gained concerning the intricate relationship between all the numbers comes from use, not pre-prepared lessons.

I sympathise with the fact that this thread is sooo long :rolleyes: Sorry about that ;)

I too have mentioned that it was only a real life problem demanding real knowledge and practice that enabled me to achieve insite into trig.

So.

The argument is not that arithmatic, tables, physics, or anything is not needed in the modern age.

It is that it is not clear what we will need most of the time. Wait till you get there, and then expend maximum energy on what is entirely relevant.

Hope this clarifies things. :)

a

[sleepies]

just because you don't "USE" information.
doesn't mean it is a waste of time or a bad idea.

information is knowledge, knowledge is power.

i might not ever use a binary number system, but learning that was a great experience and i feel it widened my mind.

i think we should focus on teaching our kids MORE not LESS.

we only use a small part of our brains. I think we should try to find ways to use the entire brain and increase learning.

PS.
how do you "Think" we got into the modern age?

we didn't get there by not doing math that is for sure.

computers can break....and people are needed to put information into computers in the first place. if you don't understand your times tables, how are you going to program a computer to solve them for you?

im so confused by this post.

[Alexander]

Originally posted by Just Wondering
It's cheaper.
You don't have to buy batteries.
You don't have the problem of getting the thing, to find that the battery is flat.
No, we don't have solar ones....
anyway, the brain enjoys it....

They still make calculators that require batteries???? :jaw




I don't know how seriously to take these comments. Either you are badly missing the wood from the trees, or giving me a good dose of sarcasm :(

I doubt you would stoop to sarcasm (hope).

Incidentally, there seems to be a mis-conception (not un-usual) that the Information Era = Technology.

It does not.

It is about problem solving, adaptability of cocepts, and salient ideas.

Hope this helps.

a

[parisfrance]

Alexander, regarding the book "Goedel, Escher, Bach" you said "never heard of them". "Them" who? If you've never heard of the books, you should definitely read them, I forgot to mention that my brother is a mathematician, just finished his PHD in math. He doesn't like any math with a practical application (read: someone will pay you to do it!! LOL my parents are SO sad). Anyway, he and many other people I know have said it's facinating, they never thought about math in the same way again. (I hate math, that's why I never read it). If the "them" you never heard of is the three guys in the name, Goedel was a mathematician, Escher is the famous artist who drew optical illusions (like two hands drawing each other), and Bach is THE Bach musician we all know.

[Britishmum]

JW, I thought your post was very funny. Sarcasm doesnt seem to be your style, am I right? I confess to not even having a calculator, I certainly have never carried one around with me.

Alexander - I don't follow the logic in waiting until you need to know something before learning it. Some things, like the abc, or number rhymes, or times tables, or a second or third language, can be learned easily through play in the early years, at the time when the brain is most able to learn. The window of opportunity then starts to close. There is no limit, as far as anyone can tell, to how much can be learned at that formative stage - it's not a case of 'learn your times tables and you won't have room to learn your alphabet or a second language.' (I have never understood, incidentally, why most schools start teaching a second language at the exact time that the window for language acquisition is closing.)

So why waste a child's brain by waiting? Knowledge is often learned, then followed later by in-depth understanding. I'm not advocating rote-learning, rather that we tap into the natural propensity of young children to learn and use methods that are in tune with their natural learning styles.

[Alexander]

file g

sleepies said:

just because you don't "USE" information doesn't mean it is a waste of time or a bad idea.



When you say "it", do you mean

1) to study

2) The the information

3) learning the information

Any way, no, you are maybe right, but it does depend upon whether it was learned willingly or not, or whether it was enjoyed.


sleepies said:
information is knowledge,



Ahh, come on sleepies! Information is only information. Data is just that. Data. It is context and relevance that turns it into knowledge.

sleepies said:
knowledge is power.


Hmm. Application of the old cliche here eh! ;)

No, sorry. Only relevant and timely knowledge is power, not knowledge in a vacuum..

sleepies said:

i might not ever use a binary number system, but learning that was a great experience and i feel it widened my mind.


But did it have to be the binary system? Why not anything else? And who decided that you should study that? In the great plan of things, all subjects are worthy of study. What makes one more relevant or important than another in the Information Era is the decision of the student to study it, not the decision of the teacher, a school, or some faceless (and probably dead) beaurocrat.

sleepies said:

i think we should focus on teaching our kids MORE not LESS.


More what? More . . . wax candle making (in case the lights go out)? How to tie a hog (so you can more easily take it to the market)? or sharpening a quill (in case biro doesn't work)? or pale mending (in case your pipes stop)? Shoe-ing a horse (essential if you it loses one on a long rocky trail, far from home)? (20th century one here) . . . using a slide rule for faster calculations. I doubt most readers even know what a slide rule is, much less remember how to use it's logarithmic functions to do multiplication?

The point is, time moves forwards, and certain skills and knowledge become redundant as technology rolls along.


sleepies said:
we only use a small part of our brains. I think we should try to find ways to use the entire brain and increase learning.


Forgive me, but this indicates a common misconception that "the more brain you have, the smarter you are or the more you can do". This is unfortunately utterly wrong. Most of the brain (in functions, if not size) deals with basic functions such as sight, digestion and animal behavior. Only the frontal lobe helps us to be what we are.

Smarts and the amount we are able to hold in a function of the way our brain cells are wired together, not the amount we have. Indeed, I would suggest that one day, it will be shown that too much brain in certain places actually makes people less smart. This is because the processing that is done in the parts of the brain with which we think is terribly local, and to reference to other parts that have more data or computed concepts is made harder by the fact that linking through too much brain is all but impossible.

Thus it is possible for people to use large amounts of their brain, but be quite dum, or use small parts of the brain, extremely efficiently, with wonderful models of the world in which they live, and be very smart.


sleepies said:
PS.
how do you "Think" we got into the modern age?

we didn't get there by not doing math that is for sure.


Brilliant point, which wonderfully re-illustrates the point that I make. Namely that the "Modern World" (Industrial World) was established and maintained by a rigorous process "pidgin holing" a number of vital skills (vital for the maintenance of the Industrial Economy) and ensuring that as wide a variety of people were exposed to this as possible. And you are right, Math (arithmetic) was an integral part of that process.

There is only one thing though.

The Industrial Age began to end in the late 60's in the US, 70's in the UK, Late 70's in Europe. In fact, out of all the industrial powers, only the Far East has yet to catch up. Now the world is moving through a kind of "overlap" time, where the "old Industrial Model Society" has to co-exist with the new "Post-Industrial or Information Era Model Society".

One of the deepest ironies of this transition is those economies that have benefited the most by using the Industrial Model for their Society and Economy, are the worsed placed to take advantage of the Information Era. This is because the mind-set required is so utterly different. In fact, I can not think of how opposite they could be!

But more on that on another post.

sleepies said:
computers can break....and people are needed to put information into computers in the first place. if you don't understand your times tables, how are you going to program a computer to solve them for you?


society will not collapse because a computer breaks, I assure you. There are all kinds of back up systems in place in case of that eventuality.

Also, I promise you, you do not need your times tables in order to be able to program well, and if you did, most programmers would find it a trivial matter to learn, or use the calculator found inside every computer;)


sleepies said:
im so confused by this post.


Er, thread you mean;)

And of course. You and most of the people who live contentedly in the Industrial Economy, oblivious of the storm that has already hit the shores.

Hope this helps

a

[Alexander]

Originally posted by Just Wondering
Yes, my calculator requires batteries.
No, I kid you not.


WOW! Really! But this explains alot about how ou see the world.
JW
why should I stoop to sarcasm?



I appologise. I was not sure. Many who encounter this thesis react in many kids of negative ways, sarcasm being second only to straight disbelief, which is understandable given that everything they know to be true, that works for them, the "solid ground" so to speak is threatened.

Forgive me.

JW
Anyway, see my post on "tables".
By the way, a penfriend in Japan just sent me a fancy one. But its so small my fingers get claustrophobia.


Stop it! You are making me giggle:p

JW
My husband says that if I bothered to go to Auckland and look in a fancy business store, I could get one.
I guess people here of my age, just don't use them that much..

And there, unintentionally, you beautifully illustrate the problem facing people who have grown up successfully in the Industrial Age, facing the idea that what worked for you should not work for the next generation. Not even to use or need a calculator demonstrates clearly that you are of the generation that did not require one, due in part because of the training you underwent.

Another generation along, and we may have kids who don't even have to use a calculator, even to get sophisticated calculations done.

But, just as surely as the knowlegde of lighting coal gas lights (essential in Victorian England) has become redundat as a life-or-death skill, so to will much of what we now regard as essential learning.

a

[truly_sarah]

A perspective to consider...

The above discussion about calculators reminds me of when the young me discovered a slide rule and instruction book in my mom's math teaching bookcase in our basement. I undertook to learn it, and there was a HUGE discussion in our house of whether I should be WASTING my time on that, because this wonderful NEW DEVICE (called the calculator) had just been invented. My dad said, well, calculators are expensive, we can't get her one, so she can use the slide rule, it's easily replaced. My mom said, well, we SHOULD buy her one because she will NEED it. But I don't think they had the money. In a year we were amazed...you could get one for FREE at Radio Shack.

My prediction is that this discussion will be replaced in another decade or sooner, by a discussion of whether our kids should get a wearable transmitter that will enable their brains to become instant calculators...whether it is OK to bypass learning arithmetic of any sort with an artificial device and whether the dependence on it is OK or not...and whether job applicants/university applicants can be asked if they have such device. Then there will be all sorts of discussions about public funding such as we are having here in Maine with the laptops in the schoolrooms and only a few pilot classrooms getting them. I have yet to see even calculators being issued to students...yet all of a sudden they are talking about issuing laptops. Well HELLO! What's up with that?

Sarah

[Alexander]

Originally posted by parisfrance
Alexander, regarding the book "Goedel, Escher, Bach" you said "never heard of them".


Silliy silly silly me.

In my semi wakefull state, I had mis-understood that these three people had each written a book!

:p

a

[Dot.mom]

Alexander wrote:
[Dot.Mom, you have no idea how close we really are. I hear you! My old man (http://www.mth.kcl.ac.uk/~streater/)

Nice Link


quote:
--------------------------------------------------------------------------------
Dot.mom said

Alexander, do tell!!!!! Math and how it is taught is something that really interests me. My father is a mathematician and taught my brother and I in a way that made public school math seem ridiculously un-inspired and limited when we finally got there. Unfortunately, we then did very poorly.
--------------------------------------------------------------------------------


Alexander wrote:
-------------------------------------------------------------------------------
Once again, the term "math" which I see as a misnomer for arithmetic. Again, the methods refined over the last 150 years are probably fine. But mathematics? That is hard. To start with, kids have to have the right mind, the curiosity that leads them in this direction. If they do not have this, you have nothing.
---------------------------------------------------------------------------------

The semantics seem the least interesting part of this whole discussion, but I guess we have to agree somewhat on terms before we can continue the discussion (or I guess we can continue to discuss terms...)

I'll give an example of how my father "taught" us "math(s)": When I was fairly young, he challenged me to a race across a chess board. The rules were that we each started out in a corner and could move our piece, in turn, one space forward or sideways, not diagonally, and we were to race to the corner diagonally opposit us. After the first match, my father declared, "we won!" (meaning we tied). We tried again, and again, "we won". We tried several different routes, but to my amazement, it didn't matter what route each of us took. It was just as fast to tranverse the sides of the board as to move one up and then one over through the middle. When I tired of this, he left me alone with the chess board and a played with counting out the squares and seeing how many fewer squares were needed if moving your piece diagonally was allowed. I remember also around this time I became obsessed with measuring the sides of triangles with a plastic ruler, which I am sure now is related.

Unfortunately, the rote drill in public school left a bad taste in my mouth and I had no desire to learn anything about anything. I remember one teacher trying to teach subtraction ot the lot of us squirming kids on a beautiful sunny fall day. She kept saying "3 take away 2 is 1" and I kept asking what happened to the 2 she took away until she finally would no longer acknowledge my question. I hadn't meant to be obstinate, but I had already learned that things don't just "go away" or vanish off the earth. Eventually my parents pulled me out and sent me to a Free School (I think they're called Democratic Schools now-same concept). It was like those years in public school never happened and I was again motivated to learn. I did memorize there, but of my own volition because I wanted the information for something else I was doing.

Gotta run!

[Alexander]

Originally posted by Britishmum
Alexander - I don't follow the logic in waiting until you need to know something before learning it. Some things, like the abc, or number rhymes, or times tables, or a second or third language, . . .

So why waste a child's brain by waiting? Knowledge is often learned, then followed later by in-depth understanding. I'm not advocating rote-learning, rather that we tap into the natural propensity of young children to learn and use methods that are in tune with their natural learning styles.

Very briefly,

the issue is not whether or not you deny the child from experiencing these subjects, but rather:

1) that we can no longer assume that these subject will have any importance to that child's future.

2) that we must ensure that children learn the "new" skills, adaptability, motivation, be self-secure etc.


Next. Why do you think that children would be wasting their brains if they are not fed this stuff? I look at it from another point of view.

We are wasting children's minds by not allowing them to develop in the manner that evolution intended.

Play.

This is the method of neural programming designed for our species that has has enabled us to do what we can do.

a

[Britishmum]

Alexander,

You have misunderstood what I meant by 'wasting' brains. I'm not talking about 'feeding' children's brains this 'stuff' - I'm talking about learning the way that they learn best, (through play) at the time when they learn best (young).

You know that I would argue that times tables are a necessary skill for the future. You say that they are not necessary for everyone, so we should wait until the individual finds that they need or want to learn them. My point was that if we wait until later, when the child/adult may decide that they would be useful, we have missed a window of opportunity to learn with ease, and so the child/adult has to 'work' to learn something that he could have learned through play. Seems foolish to me.

The 'waste' I'm talking about would be in missing this opportunity, to learn young, through play - the way that humans are intended to learn. I believe that learning through music is a form of play.

I agree one thousand percent that children should be developing the way that evolution intended. And music is one of the oldest and most natural ways to learn something, which is why I recommended it to the mother on the times tables thread. Rhythm, movement, actions, dance, music, can all combine to help the child to learn naturally, the way that I believe nature intended.

Dd is sixteen months old and I unashamedly say that we have 'started' the times tables. We sing songs such as 'two four six eight, who do we appreciate? Mummy!" as we stomp downstairs. It's fun, it's play, and it's using her natural propensity to learn. We don't do it instead of anything else, it's just one of hundreds of things we do in a day. I think it would be foolish to waste the opportunity.

[Alexander]

Essentially I agree with what you say,

except. . . .

This window of opportunity that you describe. There is a window, I agree, but it is not a window outside which we can not learn anything. There is nothing theat can not be learned by a 12 year old in short time that 4-10 year olds take, well, between 4 and ten.

The window that you describe, (actually there are 4) are the periods that the brain develops in specific ways.

Up to about two, the brain is still in it's fetal stage, that is, not yet fully grown. By one the brain has doubled in weight, that is, doubled the number of brain cells. I estimate that this is at a rate of about 100,000 cell a minute! (this is all from memory, so forgive slight errors). By 2 it has doubled again to about 2Kg.

The next stage is the amassing many trillions of connections. (yes it is indeed in the trillions!). These connections represent the sum total of all the child's experiences, and from these, a model of the world is represented in their minds. However, many of these connections create "wrong" representations of the world, which is why children sometimes say such funny things. :D It is also during this time that certain neural paths are established, and are continuously re-used. These paths

Next comes the elimination of "wrong" or un-used neural paths,

and finally, between 12 and 16ish, the execution stage. This is where cells are eliminated.

If children are able to develop a model of the world in which they learn how to learn, then they are set up to learn anything, for the rest of their lives, not only in childhood. This has to happen before they are 12.

It is worth noting here that the same is true of emotions such as empathy, concern and love, and of abstract ideas such as justice, fairness and ulturism.

If these things are not encountered and experienced in spades by the "execution stage", the connections simply will never be made, as those cells that deal with those concepts will had been deleted as "redundent" by the brain itself.

As for music, yes kids enjoy it. Your child singing 2 4 6 8 tooty tooty tooo and stomping around the floor with you is another indication of what I am talking about though.

Human children are programmed to enjoy copying the older people around them. It is a successfull evolutionary strategy. (Are they enjoying the singing or the copying;) )

But the idea that we need to take the opportunity "before it is too late" (to quote a common phrase) is to mis-understand what it is that children actually learn while we think we are "teaching". Of course they might pick up tables along the way, (and I insist that this can be done at any time), but in the Information Age, children that have learned to tackle anything that they themselves wish to, will be more usefull than children that have been "pre-trained" with certain facts.

It is not "what you know" that will be useful, but "whart you are able to take on" that will be important.

This is already true. Job descriptions in many countries ask for "self motivated" people.

I've got to get the lunch on, but this is developing into some interesting interactions.

a

[Alexander]

Sorry dot.mom,

I've just seen your post. Gotta fly, but I'll have a look later.

a

[Britishmum]

Alexander, I have always been fascinated by brain development. Although I'm not sure that you are correct that the number of brain cells doubles after birth, I believe that it was only very recently that it was found that the brain is capable of creating any new neurons after birth, and that the number is small. I once calculated that the rate of growth, if averaged out, in the womb is something like 4,000 cells per second. Wow. However you represent the figures, it is amazing. Where did you get the info on the 'fetal stage' of the brain before age two, I'd be really interested in this as I'd never read that.

I do think you are making an assumption that if one believes in helping children to learn academic things (such as times tables) in their early years, one cannot also foster metacognition, and the development of emotional intelligence. I completely agree that these are vital for this century. One aspect of learning does not - and should not - preclude the other, in fact, I believe that they should complement one another.

You are right that there are windows of opportunity for learning, and nobody could surely suggest that it is impossible to learn outside those developmental stages.Otherwise we'd all have had it by age twelve! But the fact is that it is easier to learn some things when you are young. Why make something more difficult when you need not?

As for music, I would suggest that the child enjoys the music as much as he enjoys mimicking adults. Both are natural ways of learning. You would be hard pressed to find a culture, now or in the past, that does not have music and where music is not used for learning. Music can be very much a part of play.

You conjure up an image of my toddler ("Your child singing 2 4 6 8 tooty tooty tooo and stomping around the floor with you") that seems to indicate to me that you have an mental image that is not close to the reality. If it's OK to sing and dance to 'Three blind mice' or 'Five little ducks,' why is it not OK to do the same to number rhymes where you count in multiples?

Incidentally, I still question the assertation that times tables will not be necessary for everyone this century. Just after dh and I had discussed this last night (We're finding the debate very interesting and thought provoking) he went to get a yoghurt for dd. I had bought a different brand, the smaller 'baby' ones, which come in packs of six not individually. He asked how much I'd paid for them. We then both calculated that although they seemed cheaper, they were in fact a more expensive option. We had both used our times tables extensively to come to the same conclusion.

Will our children no longer need to work out such everyday problems when they become adults? Or will those who don't know their tables just pay more and not know it?!!

I fully agree that current systems of education often miss the point, that it is knowing how to learn what you don't know that is important. Metacognition is sadly missing in many of todays 'educated' people. However, on the bright side there are many teachers who understand these issues - you only have to visit the boards for teachers on brain based or accelerated learning to see the interest and expertise in our classrooms.

Also I agree about self-motivation, I think that Kohn hits the nail on the head, although I find some flaws in some of his reasoning. But that's a whole new topic............

fascinating discussion, by the way!

[Alexander]

file h

Dot.mom Said:



The semantics seem the least interesting part of this whole discussion, but I
guess we have to agree somewhat on terms before we can continue the
discussion (or I guess we can continue to discuss terms...)

Terms now discussed here:

Real Mathematics. (Not "Math") (http://mothering.com/discussions/showthread.php?s=&threadid=5030)

Dot.mom Said:

I'll give an example of how my father "taught" us "math(s)": When I was fairly young, he challenged me to a race across a chess board. The rules were that we each started out in a corner and could move our piece, in turn, one space forward or sideways, not diagonally, and we were to race to the corner diagonally opposite us. After the first match, my father declared, "we won!" (meaning we tied). We tried again, and again, "we won". We tried several different routes, but to my amazement, it didn't matter what route each of us took. It was just as fast to traverse the sides of the board as to move one up and then one over through the middle. When I tired of this, he left me alone with the chess board and a played with counting out the squares and seeing how many fewer squares were needed if moving your piece diagonally was allowed.



Perfect. Funny actually. My dad did exactly the same thing!!! :D So good in fact, I will quote this in Lesson Plans for Mathematics. (http://mothering.com/discussions/showthread.php?s=&threadid=5144)


Dot.mom Said:

Unfortunately, the rote drill in public school left a bad taste in my mouth and I had no desire to learn anything about anything. I remember one teacher trying to teach subtraction ot the lot of us squirming kids on a beautiful sunny fall day. She kept saying "3 take away 2 is 1" and I kept asking what happened to the 2 she took away until she finally would no longer acknowledge my question. I hadn't meant to be obstinate, but I had already learned that things don't just "go away" or vanish off the earth. Eventually my parents pulled me out and sent me to a Free School (I think they're called Democratic Schools now-same concept). It was like those years in public school never happened and I was again motivated to learn. I did memorize there, but of my own volition because I wanted the information for something else I was doing.



Kids want to use their minds. They enjoy it. They develop that way. Your dad provided the environment. Unfortunately, the school you went to tried to "teach" you something altogether different. What a waste. Totally cool that you got to go to a Free School. My folks very nearly did too. I don't know why that did not happen:(.

As for Free School = Democratic School. That is not accurate. A free school is run by adults for children to do as they please. At a Democratic School, the children to do as they please, but the children run the school for themselves, and employ adults to help create and maintain the right environment.

Dot.mom, you're on my buddy list;)

a

[Alexander]

Originally posted by Britishmum
Alexander, I have always been fascinated by brain development. Although I'm not sure that you are correct that the number of brain cells doubles after birth, I believe that it was only very recently that it was found that the brain is capable of creating any new neurons after birth, and that the number is small.




I checked. ;)

Brain weight is directly proportional to No. of brain cells.

Brain increases between 2 and 3.5 times between 0 and 2.

Brain cell production peaks at 250,000 per min!!! :jaw

The figures ARE amazing aren't they.

BM said:

I do think you are making an assumption that if one believes in helping children to learn academic things (such as times tables) in their early years, one cannot also foster metacognition, and the development of emotional intelligence.

Unfortunately, not an assumption. The casually observed tendencies in children are all around us, (much resourses in the current bulky Industrial Model Education System is designed to either pick up the pieces where it fails with "special educators", drugs and theropists, or to co-erse children ever more effectively to comply with the will of the "Body Corporate"), and teachers whose eyes are still above the water know it.

Whether or not it is a straight line graph, or gradual decline with a catastrophic fall in the middle, I don't know, but one thing is for certain. More study does not equal better accedemic results, or better understanding, but you do get kids with NO motivation, and ofter little or no empathy, tolerance, creativity or common sense.

This is the story everywhere in Japan, where the Industrial Education Machine has been taken to an extreme.

BM spake:

You are right that there are windows of opportunity for learning, and nobody could surely suggest that it is impossible to learn outside those developmental stages. Otherwise we'd all have had it by age twelve! But the fact is that it is easier to learn some things when you are young.

1) The windows that exist do close. But they close, not for learning "things", but for "how to learn how to do things", which is what I want people to realize is one of the most important skills to have in the InformationEra.

2) otherwise we would have to have it by 12. Exactly, but I take issue with this idea that it is easier to learn "things" while you are young. It does not. Children are patient learners while they are interested.

"If it's OK to sing and dance to 'Three blind mice' or 'Five little ducks,' why is it not OK to do the same to number rhymes where you count in multiples?"

I have never indicated this. But I know you would agree that you would stop immediately that he wanted to. A child in "class" at school does not have the same power, or choice. Secondly, songs and stomping are perhaps non-effective methods of teaching older children everything that is considered important to children in the age range, say 6 - 12!!! ;)

"Incidentally, I still question the assertation that times tables will not be necessary for everyone this century."

There is no such assertion. The idea is that there may not be and there may well be requirements for many other "facts". The ability to re-train, adapt, land recognise what the relevent facts are, are the skills our children need.

On your yoghurt story, I can only say that you are products of the Industrial Age. ;) It might be posible for an Information Era person to do the same calculation in the same way, but more likely it would not matter that he could not. What matters is the they are able to find a way to get at the same result. And a calculator might very well be the implement used, (or it could folding bits of paperor who knows???)

Of course our children may need to work out such everyday problems when they become adults. But the methods of solving will be designed by them. It may even be that they find it easier to do all this stuff by learning their tables tables, but I think it more likely they will just pay more, and not care.

"However, on the bright side there are many teachers who understand these issues"

This, unfortunately goes nowhere to enlightening the parents, the school boards or the State Education Councils. We are lonely soldiers, fighting to keep the children thinking. The course I designed is to get children thinking again. Once they are doing that, they learn English all by themselves. It's magic. It works. If parents "discovered what I was doing, or what I was not doing, I'd go bankrupt in a week:(

a

[Dot.mom]

Originally posted by Alexander
[As for Free School = Democratic School. That is not accurate. A free school is run by adults for children to do as they please. At a Democratic School, the children to do as they please, but the children run the school for themselves, and employ adults to help create and maintain the right environment.


a [/B]I never new there was a distinction, which I guess is proof how well our Free School did. I thought we did run the school!!!! But now that you mention it, we did not practice voting for any major decisions, only minor ones (like naming the guinea pig-"Stench" poor thing, or where to go on field trips). I do wish we had either a Free School or a Democratic School in this area for our daughter.

[Britishmum]

Alexander,

Do you have a link for the info about brain cell growth? My searches only throw up the recent research showing that the brain can grow new cells, which challenges the old assumption that all, or almost all, cells were in place at birth.

I entirely agree that the ability to learn and to know how to learn is more important than the content of what you learn. Also I am convinced that emotional intelligence is more important than IQ. However, I am still not convinced that this means that learning things such as the times tables precludes a child from becoming emotionally intelligent. I believe that is is how these things are learned that is of vital importance.

As I said, I do not advocate 'stomping' around the room chanting times tables! I'm talking about tapping into the natural way that the brain learns. That means using multi-sensory means and being mindful of all forms of intelligence (Gardner's multiple intelligences being a good model here.) Using music is a part of this, but not stomping and rote learning! It's called 'play' - which we both agree is vital for effective learning.

Music is also used effectively by many teachers with older children in the age range you talk about, ie 6 to 12. Physical movement is sadly not used enough in many classrooms, ignoring the brain's need for movement. Again, I am not advocating the learning of times tables in place of investigations and practical maths, but I believe that things like this can be incorporated into a child's day in a way that gives movement, a break, and FUN!

You say that your assumption that helping children to learn academic things precludes them becoming emotionally intelligent or metacognitive, is not an assumption: "The casually observed tendencies in children are all around us"

Can the apparent lack of emotional intelligence in children around us be attributed entirely to the content of what they learn, or maybe to the way that the learning occurred? Personally, I think that the method of learning is the deciding factor. I'm sure that a lot of inappropriate material is covered in schools, but it is the method of delivery that is more likely to lead to poorly motivated children.

I also think that there are also a lot of other factors that lead to unmotivated youngsters, other than the failings of a school. There are many many reasons for a child lacking in emotional intelligence - not least, being raised by parents who lack it themselves! Maybe home schooling is ideal, but what about children whose parents lack this motivation or emotional intelligence? Which children will end up with a lower EQ, those who are raised by parents with low EQs, or those attending imperfect schools?

You are right that children in schools do not always have the opportunity to say no to the learning diet being offered themm and you paint a sad picture of schools. I am more of an optimist, and believe that there are some amazing teachers out there who do strive to understand these issues. They have to work around increasingly stringent legislation nowadays, which makes their job harder, but I believe that it is still possible to deliver a curriculum in a way that fosters the qualities that I think we both agree are essential for the adults of the future.

Maybe children in the future won't care that they can't work out things like the cost of their groceries,or how to split the bill in a restaurant. How sad! I cannot imagine anything more frustrating than being unable to do such a simple calculation in my head and having to get out a gadget to do something that my brain could do with ease if it had been given practice.

[Britishmum]

Alexander, I've searched some more and still can't find a reference anywhere to brain size being proportional to the number of brain cells. Every reference I have read states that all neurons are in place by birth, or 'almost all', or 'essentially all'. Hence the excitement of last years research showing that the brain can form new cells, and its implications for treatment of conditions such as Altzeimers.

I thought that brain growth (ie size increase) after birth is due primarily to continued myelination and the phenomonal rate of synaptic connections being made.

I'm happy to be corrected though, do you have a reference for your theory?

[Alexander]

Originally posted by Britishmum
Alexander,
Do you have a link for the info about brain cell growth? My searches only throw up the recent research showing that the brain can grow new cells, which challenges the old assumption that all, or almost all, cells were in place at birth.

No, you are right. I may have made an incorrect assumption that increased weight = increased number of cells. Why should it not? but anyway, a quick search thew up this:
Neuroscience for Kids - Brain Development (http://faculty.washington.edu/chudler/dev.html)

a

[Alexander]

I still think the number of cells increase, because the fetal brain is capable of cell division.

a

[Britishmum]

Alexander, thanks for the link.

That confirmed what I thought, that there may be a very small increase in neurons after birth, but essentially they are all there. Their job after birth is to get to work, or to die off.

Phew, I thought I'd been getting it wrong all these years. Just like those scientists who just found out that the adult brain DOES produce new neurons anyway!

[SagMom]

Hey, I found this book at the library yesterday and immediately thought of this thread. The book is: The Five Faces of Genius--The Skills to Master Ideas at Work by Annette Moser-Wellman.It is geared toward the business worker and the "thinking skills" that one needs to be sucessfull. Is anyone familiar with this book? According to the jacket, the author owns a consulting firm that "offers workshops in creative business thinking." The "Five Faces" that she writes of include things such as: being able to visualize in detail, being able to observe details in things around us, finding connections between seemingly unrelated things, having perseverance and taking risks, being able to simplify or "distill ideas to the essence."

It amazed me that adults were getting together to be taught these things...to me, it all boils down to creativity and problem-solving. It would seem to me that life, in general, would offer us many opportunities to develop these skills and that classes to learn these skills wouldn't be necessary. However, some big name companies are using her services and her book got published, so I may be wrong---what do you all think? Are these skills that need to be TAUGHT?

[Britishmum]

Joan, this book sounds interesting.

I think that these are skills that should be fostered, rather than 'taught'. I don't think you can teach things like perseverence, or resilience, or visualization. But you can foster them - or not - in a learning environment, or in a work environment, as this author writes about. With regards to education, I think that teachers need to be mindful about these sorts of qualities when they plan lessons. Content can be delivered in numerous ways, only some of which will foster these lifelong qualities in students.

[lorrielink]

im just being a trouble maker today and bumpin stuff :wink

[beansricerevolt]

Yes, very old thread!

subbing so I can come back and read :)

[saintmom]

Old thread,but info that needs to be restated OFTEN!

www.keypress.com Offers miquon,algebra and geometry from a deductive rather than inductive approach.

[Aeress]

I am glad this got bumped. I didn't realize that this conversation was from 2002. It is interesting to me that I was reading this same information a few days ago, it was a recently published article, so I assumed it was new research but considering the original thread is about six years old, it is not a new idea.

So, what has happened in the six years since this thread was started? Has anyone seen real progress in the system of public school?

[Oriole]

I wouldn't call forgetting numbers a progress, nor do I agree with all the "new stuff" that pops up. I do notice the dumbing down of what is taught, and shift to intuition in mathematics rather than on concrete numbers and logic in the classroom. To be honest, it drives me crazy...

I think of saying "they don't have to know it" as a very dangerous thing. I have kids who are coming in to 6th grade without being able to multiply or divide without a calculator, and that's scary to me, and nothing to be happy or proud about.

There is a beauty in concrete numbers, and abstract concepts. And you can teach them all the other stuff in other classrooms, but for Pete's sake, don't pull the numbers and basic skills from the curriculum in mathematics! Believe it or not, I TOO want them to develop their problem solving skills, and their abstract skills, and whatnot, but NOT in the name of sacrificing centuries of knowledge in number relationships...

I don't like when people say "let's not teach them... because they don't need it..." That's what I used to say in middle school, and I thank my parents and teachers for patiently explaining to me, that yes, I will need it, just maybe I don't realize it right now.

On top of that, I do think that there is some benefit to brain development, since there is nothing as abstract in the curriculum as numbers. Everything else is language based, and numbers seem to provide that balance for developing that other side of our brain. I truly believe that meaningful mathematics program develops a child in the ways that we don't realize. It would be a BIG mistake to skip that part in education.

Soo... if US goes on this crazy spin and stops teaching basic skills in math, I'd be only too happy to teach my kids what I think they should know, and I'm sure that will mean heck of a lot more oppotunities open to them in the future. Imagine math becoming a dead language... *shudder*

[beansricerevolt]

I do agree with what Alexander is saying but feel their needs to be a balance. Numbers are our essence. Everything we've come to know is or can be encoded by numbers (Fibonacci numbers come to mind). We were created with numbers in mind :) I think its only natural we learn to manipulate them.

[graken]

This Math, Maths and Mathematics is quite simple they all mean the same thing.
With Math the American abbreviation and Maths the British abbreviation of Mathematics.

The confusion is maths is used differently by the informed to its common usage.

When those with mathematical training mean finding patterns and relationships when they talk of math(s/ematics). Which are often expressed with weird symbols.

They refer to different branches by different names such as Arithmetic, Geometry, Algebra, Set Theory, Calculus, etc. All the branches are part of mathematics.

Some mathematicians dislike how most people use terms and try to distinguish between their usage and common usage by making a distinction between the mathematics and math(s) or just math.

Regarding teaching maths so the relationships are discovered. Their are a few methods:

Montessori uses materials which make relationships clear so they can be discovered.

My favorite teacher would set projects such as investigating the lengths of right angled triangles, at some point he would suggest we squared the lengths at some point someone would go ah! Followed by the rest of the class.

My class used cards to learn when we were small. Which showed new ways of doing things and we would answer questions to test we understood it. This was not true mathematical inquiry but concepts have to be introduced some how. We were the ones that had ah moments.

Times tables are fundamentally a bad idea, I was fortunate that I could calculate the answers fast enough to fool me teachers into thinking I could remember them. Better techniques than those that I used can be found by search for:
Trachtenberg Arithmetic
I think every child should be introduced to these techniques rather than using times tables. Beads on a board would be a good tool to try and develop ah moments.

Teachers that say you can't do something such take a bigger number from a smaller or square root a negative number do a disservice. But their is fundamentally a problem that we for the most part use vectors yet some relations have scalar definitions. Complex/imaginary (what awful names as well; aren't all numbers imaginary) numbers are a result of this ugly usage confusing many children and adults for no reason. Understood in terms of set theory it is quite simple but most university science students are not aware of it. Children are suppose to have excellent intuitive understanding of sets yet we demonstrate daft asymmetric functions on vector quantities.:irked: The result is confusion regarding what is happening to begin with followed with confusion as to why this is taught subsequently once what is happening is understood.
Another thing which is not clear is the difference between transitive and intransitive operations. :angry
I argued with my teachers at school about these things (they felt wrong) but only now do I understand explicitly why I was right. Many branches of maths were developed independently and are in-fact subsets of more comprehensive branches of maths. Some of the definitions are rather arbitrary and hence poor. Roll on a more sensible approach to maths education.
Charles